This section presents three other possible couplings between bosonic dark matter fields and nuclear spins [1]}, [2]}, [3]}, [4]}, [5]}: the quadratic wind coupling with the axions, the couplings to dark electric field and magnetic field mediated by spin-1 bosons such as dark photons [4]}, [5]}. The Hamiltonian of the three couplings can be written as
\(&\mathcal {H}_{\textrm {quad}} \approx 2\textrm {g}_{\textrm {quad}}^2\hbar ^2 c^2 \dfrac{\rho _{\textrm {DM}}}{2\pi \nu _{a}}\sin (2\pi \nu _a t) \mathbf {v} \cdot \textbf {I}_{\rm {N}},\\&\mathcal {H}_{\rm {dMDM}}\approx \textrm {g}_{\rm {dMDM}} \sqrt{2 \hbar ^3 c \rho _{\rm {DM}}} \sin (2\pi \nu _{a}t) \mathbf {v} \cdot \textbf {I}_{\rm {N}},\\&\mathcal {H}_{\rm {dEDM}}\approx \textrm {g}_{\rm {dEDM}} \sqrt{2 \hbar ^3 c \rho _{\rm {DM}}} \sin (2\pi \nu _{a}t) \mathbf {v} \cdot \textbf {I}_{\rm {N}} /|\mathbf {v}|,\) 
